1. Consider the joint pdf f(x, y) = 3(x² + y)/11 for ) < x < 2, ) < y < 1. (a) Plot the joint pdf f(x, y). (b) Show that the marginal pdf of X is fa (x) = 3(2x² + 1)/22 for 0 < x < 2. Plot fa(x). (c) Derive the marginal pdf of Y, fy(y). Plot f,(y). (d) Derive the conditional pdf of Y given X, f(y|x). Plot f(y|x) for X = 0, 1,2. (e) Derive the CEF of Y given X. (f) Calculate E(X), E(Y), E(X²), E(Y²), E(XY), Var(X), Var(Y), Cov(X,Y). (g) Find the best linear predictor of Y given X. (h) Plot the CEF and BLP as a function of X.
1. Consider the joint pdf f(x, y) = 3(x² + y)/11 for ) < x < 2, ) < y < 1. (a) Plot the joint pdf f(x, y). (b) Show that the marginal pdf of X is fa (x) = 3(2x² + 1)/22 for 0 < x < 2. Plot fa(x). (c) Derive the marginal pdf of Y, fy(y). Plot f,(y). (d) Derive the conditional pdf of Y given X, f(y|x). Plot f(y|x) for X = 0, 1,2. (e) Derive the CEF of Y given X. (f) Calculate E(X), E(Y), E(X²), E(Y²), E(XY), Var(X), Var(Y), Cov(X,Y). (g) Find the best linear predictor of Y given X. (h) Plot the CEF and BLP as a function of X.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:1. Consider the joint pdf
f (x,y)
= 3(x² + y)/11
for
0
) < x < 2, () < y < 1.
2.0
(a) Plot the joint pdf f(x, y).
(b) Show that the marginal pdf of X is
f#(x) = 3(2x² + 1)/22
for
0 < x < 2.
Plot f.(x).
(c) Derive the marginal pdf of Y, f,(y). Plot f,(y).
(d) Derive the conditional pdf of Y given X,f(y|x). Plot f(y|x) for X = 0, 1,2.
(e) Derive the CEF of Y given X.
(f) Calculate E(X),E(Y), E(X²), E(Y²), E(XY), Var(X), Var(Y), Cov(X,Y)
(g) edictor of Y given X.
Find the beşt linear pr
(h) Plot the CEF and BLP as a function of X.
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